Effect of lumen size on the effective transverse thermal conductivity of unidirectional natural fiber composites

A precise square arrayed pipe filament (SAPF) model is developed to predict the effective transverse thermal conductivity of unidirectional natural fiber composites based on thermal–electrical analogy technique. The dimensionless effective transverse thermal conductivity Kt+ is found to be expressed as a function of the geometrical ratio (α, 0 < α < 1) of lumen radius (rl) to fiber radius (rf), ratio (β) of thermal conductivities of fiber (Kf) to matrix (Km), and fiber volume fraction Vf. The analytical results showed that, as the Vf   increases, Kt+ can be changed in two ways: (1) Kt+ increases when α is smaller than a critical value αc  ; (2) Kt+ decreases when α is larger than αc. The critical value αc depends only on the value of β, in addition a smaller β leads to a smaller αc and the value of αc approaches to 0.685. Thermal conductivity of unidirectional natural fiber composites is significantly affected by lumen size ratio α. It is concluded that unidirectional thermal insulation composite can be designed by choosing the fiber with α > αc, and thermal conduction composite with α < αc.